What is the Greatest Common Factor of 5805 and 5824?

Greatest common factor (GCF) of 5805 and 5824 is 1.

GCF(5805,5824) = 1

We will now calculate the prime factors of 5805 and 5824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5805 and 5824.

How to find the GCF of 5805 and 5824?

We will first find the prime factorization of 5805 and 5824. After we will calculate the factors of 5805 and 5824 and find the biggest common factor number .

Step-1: Prime Factorization of 5805

Prime factors of 5805 are 3, 5, 43. Prime factorization of 5805 in exponential form is:

5805 = 3³ × 5¹ × 43¹

Step-2: Prime Factorization of 5824

Prime factors of 5824 are 2, 7, 13. Prime factorization of 5824 in exponential form is:

5824 = 2⁶ × 7¹ × 13¹

Step-3: Factors of 5805

List of positive integer factors of 5805 that divides 5805 without a remainder.

1, 3, 5, 9, 15, 27, 43, 45, 129, 135, 215, 387, 645, 1161, 1935

Step-4: Factors of 5824

List of positive integer factors of 5824 that divides 5805 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 182, 208, 224, 364, 416, 448, 728, 832, 1456, 2912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5805 and 5824. The biggest common factor number is the GCF number.
So the greatest common factor 5805 and 5824 is 1.

Also check out the Least Common Multiple of 5805 and 5824